def noisy_r(i, d):
"""
Calculate the Pearson r value for a noisy image with noisy intensities.
"""
i_o = i + np.random.normal(0, intensity_typical_error, size=len(i)) * i
n = np.array([
np.random.normal(
0,
np.sqrt(D / number_of_measurements_per_stack) + read_noise)
for D in d
])
d_n = d + n
r = lin.pearson_r_single(i_o, d_n, saturate)
return r
# Loop over the cameras and their associated data
for camera, ax_column, intensities, intensity_errors, means_raw, means_jpeg in zip(
cameras, axs.T, intensities_all, intensities_error_all,
mean_raw_all, mean_jpeg_all):
# Select the mean data from the relevant channel only
# This is very clunky (double for-loop and still using an index anyway)
# It might be better to change the way data are loaded (e.g. per
# channel instead of per camera) reverse the order of these for-loops
mean_raw_c = means_raw[:, j]
mean_jpeg_c = means_jpeg[:, j]
# Calculate Pearson r values of the RAW and JPEG data
# These are added to the plot titles
r_raw = lin.pearson_r_single(intensities,
mean_raw_c,
saturate=0.95 * camera.saturation)
r_jpeg = lin.pearson_r_single(intensities, mean_jpeg_c, saturate=240)
# Plot title, including device name and r values calculated above
title = camera.name + "\n" + "$r_{JPEG} = " + f"{r_jpeg:.3f}" + "$ $r_{RAW} = " + f"{r_raw:.3f}" + "$"
# Fit a linear function to the RAW response and an sRGB function to the
# JPEG response, to plot as lines
x = np.linspace(0, 1, 250)
non_saturated_indices_raw = np.where(
mean_raw_c < 0.95 * camera.saturation)
fit_raw = np.polyfit(intensities[non_saturated_indices_raw],
mean_raw_c[non_saturated_indices_raw], 1)
line_raw = np.clip(np.polyval(fit_raw, x), 0, camera.saturation)
bit_number = 12
max_value = 2**bit_number - 1
saturate = 0.95 * max_value
# Bias and read noise characteristics
bias = 528
read_noise = 10 # ADU
intensity_typical_error = 0.05 # %
# Camera response under perfect, noiseless conditions
intensities_real = np.linspace(0, 1, number_of_intensities)
digital_values = bias + intensities_real * (max_value - bias)
# Observed r under perfect, noiseless conditions
r_pure = lin.pearson_r_single(intensities_real, digital_values, saturate)
print(f"Pearson r on pure I, M: {r_pure:.3f}")
# Add an observation error to the intensity (e.g. uncertainty in exposure time
# or in polariser angle)
intensities_observed = intensities_real + np.random.normal(
0, intensity_typical_error, size=len(intensities_real)) * intensities_real
r_noisyI = lin.pearson_r_single(intensities_observed, digital_values, saturate)
print(f"Pearson r on noisy I, pure M: {r_noisyI:.3f}")
# Add a measurement error in the camera response
noise_ADU = np.array([
np.random.normal(
0,
np.sqrt(D / number_of_measurements_per_stack) + read_noise)
for D in digital_values